Brown delivered his decision to Aberdeen chairman Stewart Milne on Monday night, two days after the sixth goalless draw of the season at Pittodrie, against Motherwell, left the Dons in ninth place in the Clydesdale Bank Premier League with three games until the split.
Aberdeen will face Celtic at Parkhead on Saturday at least two points off the top six - Hibernian could extend the gap when they face Motherwell on Friday night - after taking two points from their last three games.
The 72-year-old's contract expires at the end of the season but Brown insisted it was his decision alone to move aside.
Brown, whose assistant Archie Knox will leave the club in the summer, said: "This has been a delight, this job. The dressing room and the response has been exceptional, the goodwill from the fans has been consistently exceptional.
"You have a shelf life in any job. My intention was to wait until the end of the season but then I thought it was unfair to spring it upon the club.
"Archie and I still have the ambition to take this club into the top echelons of the league and we have not ruled that out, far from it.
"I wouldn't want anyone to think I am retiring because we don't think we are going into the top six.
"Two of the last three games have been very good. The quality against Kilmarnock was very good and we created four or five chances against Motherwell, the second best team in Scotland. We had a disappointment against Ross County in between."